I would bet it is not the Twitter app using the battery so much but the internet access needed to use the app that is draining the battery. I also don't think another app would reduce the battery drain from mobile internet access. Basically it is just a given that internet access requiring apps will always use alot of battery power.

The only thing that will reduce the battery usage is a Twitter app that lets you reduce how often it accesses the internet checking tweets but that will just delay you getting your tweets.